![]() ![]() In short, to solve the problem of size n, Strassen’s approach creates seven problems of size (n – 2). Whereas Strassen’s approach performs seven multiplications on the problem of size 1 x 1, which in turn finds the multiplication of 2 x 2 matrices using addition. The conventional approach performs eight multiplications to multiply two matrices of size 2 x 2. STRESSEN_MAT_MUL (A + 3 * (n/4), B + 3 * (n/4), C + 3 * (n/4), n/4)Įnd Complexity Analysis of Matrix Multiplication using Divide and Conquer approach Algorithm Algorithm STRESSEN_MAT_MUL (int *A, int *B, int *C, int n) Similarly we can derive all C ij for strassen’s matrix multiplication. This is same as C 12 derived using conventional approach. It takes more space for storing sub matrices.Let us check if it is same as the conventional approach. It is not practically possible as it is computation and theoretical approach only. When the matrix is sparse this method works fine because sparse matrices take less time to compute. R2, c2 = r // 2, c// 2 return mat, mat, mat, matĬ = np.vstack((np.hstack((c11, c12)), np.hstack((c21, c22))))įrom the above we see that Strassen’s method is looking good, but it is good to remember is that it is not often used for matrix multiplication for five reasons:Ĭonstraints used in the above method are generally very large it takes more time in computation. In the first part we split our matrices into smaller matrices and in other functions we perform Strassen’s method of operation, which we see in the above formula of scalar addition and subtractions of the scalar. Pi=AiBi =(α1ia+α2ib+α3ic)(β1ie+β2if+β2ig) Where a,b ,β,α are the coefficients of the matrix that we see here, the product is obtained by just adding and subtracting the scalar.īelow is the code implementation using Python, divided into two parts. We do not exactly know why we take the row of one matrix A and column of the other matrix and multiply each by the below formula. Submatrix Products: We have read many times how two matrices are multiplied. Now compute the r,s,t,u submatrices by just adding the scalars obtained from above points. Recursively compute the seven matrix products Pi=AiBi for i=1,2,…7. Using the formula of scalar additions and subtractions compute smaller matrices of size n/2. Steps of Strassen’s matrix multiplication:ĭivide the matrices A and B into smaller submatrices of the size n/2xn/2. It takes only seven recursive calls, multiplication of n/2xn/2 matrices and O(n^2) scalar additions and subtractions, giving the below recurrence relations. T(n)=O(n^3) Thus, this method is faster than the ordinary one. T(N) = 8T(N/2) + O(N2) From the above we see that simple matrix multiplication takes eight recursion calls. Using these equations to define a divide and conquer strategy we can get the relation among them as: Now from above we see: r=ae+bg s=af+bh t=ce+dg u=cf+dhĮach of the above four equations satisfies two multiplications of n/2Xn/2 matrices and addition of their n/2xn/2 products. We will divide these larger matrices into smaller sub matrices n/2 this will go on. Suppose we have two matrices, A and B, and we want to multiply them to form a new matrix, C.Ĭ=AB, where all A,B,C are square matrices. For larger matrices this approach will continue until we recurse all the smaller sub matrices. Here we divide our matrix into a smaller square matrix, solve that smaller square matrix and merge into larger results. Matrix multiplication is based on a divide and conquer-based approach. The time complexity of this algorithm is O(n^(2.8), which is less than O(n^3). This article will focus on Strassen’s multiplication recursive algorithm for multiplying nxn matrices, which is a little faster than the simple brute-force method. Here we will use a memoization technique based on a divide and conquer approach. We also have fast algorithms using dynamic programming. Some are slow, like brute-force, in which we simply solve our problem with polynomial time. We have seen a lot of algorithms for matrix multiplication. ![]()
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By default, the objects are drawn in the active canvas. 11.2.2.2 With C++ Statements (Programmatically)įrequently we want to draw in different canvases or pads. In case of canvases or pads, the border becomes highlighted when it is active. To interactively make an object “active”, you can use the middle mouse button. Some objects may become “active” objects, which mean they are reordered to be on top of the others. Objects in a canvas, as well as in a pad, are stacked on top of each other in the order they were drawn. 11.2.2 Selecting Objects 11.2.2.1 The Middle Mouse Button Why is that? In short, the canvas is not updated with each change for performance reasons. This should change one of the coordinates of our line, but nothing happens on the screen. For example, try to do: root a.SetX1( 0.9) How would one move an object in a script? Since there is a tight correspondence between what is seen on the screen and the object in memory, changing the object changes it on the screen. Rotating: 11.2.1.2 With C++ Statements (Programmatically) Resize (exists also for the other directions): The cursor changes its shape to indicate what may be done: 11.2.1.1 The Left Mouse ButtonĪs was just seen moving or resizing an object is done with the left mouse button. First, let’s see how it is done in the GUI. 11.2.1 Moving, Resizing and Modifying ObjectsĬhanging the graphic objects attributes can be done with the GUI or programmatically. As said, interacting with an object on the screen changes the object in memory. You do not obtain the same result as before, the coordinates of ‘ a’ have changed. Now move it interactively by clicking with the left mouse button in the line’s middle and try to do again: root a.GetX1() X1 is the x value of the starting coordinate given in the definition above. You can try for instance to look at the starting X coordinate of the line: root a.GetX1() One actually interacts with the real object, not with a copy of it on the screen. One very important characteristic of ROOT is that transforming an object on the screen will also transform it in memory. For example, the line drawn in the previous paragraph may be moved or transformed. When an object is drawn, one can interact with it. A default canvas is drawn since there was no opened one. ![]() The first statement defines a line and the second one draws it. If no canvas is opened, a default one (named “ c1”) is instantiated and is drawn. This instructs the object “ object” to draw itself. One draws an object in the active canvas by using the statement: object.Draw() If several canvases are defined, there is only one active at a time. The basic whiteboard on which an object is drawn is called a canvas (defined by the class TCanvas). This class has a virtual method Draw() so all objects are supposed to be able to be “drawn”. In ROOT, most objects derive from a base class TObject. Plots and histograms are discussed in a chapter of their own. In this chapter, we are going to focus on principals of graphics and 2D objects. Graphical capabilities of ROOT range from 2D objects (lines, polygons, arrows) to various plots, histograms, and 3D graphical objects. 11.10.2 Writing Several Canvases to the Same PostScript Fileġ1 Graphics and the Graphical User Interface.11.5.6 Orientation of Tick Marks on Axis.11.5.5 Drawing Axis Independently of Graphs or Histograms.11.5.2 Axis Options and Characteristics.11.4.6 Text and Latex Mathematical Expressions.11.4.5 Curly and Wavy Lines for Feynman Diagrams.11.3.3 Converting between Coordinate Systems.11.3 Graphical Containers: Canvas and Pad.11.2.4 Executing Events when a Cursor Passes on Top of an Object.11.2.3 Context Menus: the Right Mouse Button.11.2.1 Moving, Resizing and Modifying Objects.11.2 Interacting with Graphical Objects.11 Graphics and the Graphical User Interface. ![]() ![]() ![]() To reduce costs, Alice and Bob agree to use a more efficient data transfer method by using a special alphabet, which replaces every “six digits” with one “letter”. The second problem is that the tariffs for phone calls are too expensive and dictate each byte as 8 binary digits will last too long. In this case, Alice may convert the image into the binary system and dictate to Bob the binary digits (bits), after that he will be able to convert them back to the original image. The first problem is that she cannot simply describe how the image looks, because Bob needs an exact copy. To figuratively understand why Base64 was invented, imagine that during a phone call Alice wants to send an image to Bob. Thanks to it, you can convert Chinese characters, emoji, and even images into a “readable” string, which can be saved or transferred anywhere. What is Base64?īase64 is a encoding algorithm that allows you to transform any characters into an alphabet which consists of Latin letters, digits, plus, and slash. Now if you have a base64 string and want to decode it to the original aspect ratio, how do you do that? In this article, we are going to discuss the different methods to convert base64 to images on your Windows 11/10. The main objective is to prevent a file or an image from being corrupted during transmission. It is mainly used when you need to encode binary data which is to be recorded and sent on media which process ASCII. How to convert Base64 to Images in WIndow 11/10īase64 is a binary-to-text encoding scheme used to encode files and images by translating them into a radix-64 representation and presenting the binary data in an ASCII string format. ![]() ![]() ![]() ![]()
![]() ![]() How it works: Glyphs is easy to use and has an extensive array of options, even the “mini” version. This is the font-building software I use. But the feature that sets this one apart from the others I’ve mentioned so far is the ability to create color fonts, a newer font file type that gives the user control over color and shading variations for individual glyphs.įormat and price: Mac app $50 for Glyphs Mini, $300 for Glyphs full version (Trial available Student & Educator discounts available)įile types: OTF and WOFF (webfont) for mini, full version exports OTF, TTF, UFO, Webfonts (EOT, WOFF, WOFF2), Colorfonts, Metrics You create letters (or glyphs) in Illustrator or Photoshop and then drag the letters into the extension, where it compiles the complete font set.įontself has a lot of tools you’d need to build a comprehensive font, like the ability to create alternate characters, ligatures, and fine-tuning spacing and kerning. ![]() How it works: This one is an extension for Illustrator and Photoshop. *Note that the Windows version of this app is not as robust as the iPad version.įormat and price: desktop extension $49 for Illustrator-only, $98 for both Photoshop and Illustrator (Student & Educator discounts available)įile types: OTF, OpenType-SVG, WOFF (webfont) You can also share your font on the developer’s website. When you’ve finished building your font, you can export (ttf) so you can install it on your tablet or desktop. One solid benefit to this tool is that it has both a freehand tool and a bézier tool so you can get really defined curves and straights (a bit like building letters in Illustrator). You can also adjust kerning and letter spacing. There are several pen and stroke options so you can fine-tune your glyph drawings. How it works: Draw each letter in the app using a large character reference set that includes Latin, Greek, and Cyrillic letters. Other paid features include more letter variations, ligature options, and font storage on the Calligraphr server.įormat and price: Tablet app $8 for iPad and $5 for Windows tablets* If you want any extended options like the ability to adjust the spacing, leading, or add extra characters, then you’d pay the monthly subscription fee. How it works: You print off font-building template pages, use a pen to fill out the characters, scan into the computer (or take a photo), upload it to the Calligraphr webpage, and they automatically convert it to font files (ttf and otf). I didn't find it the easiest program to navigate around, but if you invest some time getting to know the tools and keyboard shortcuts, then then this is a great app to create your first font from beginning to end.įormat and price: web-based service free to use, $8/month for extended options It's a very advanced editor with lots of options that you would see in the more expensive programs. When you’ve built your alphabet you can share on the Fontstruct website and download (ttf) to use on your own computer.įormat and price: Free (Donations welcome)įontForge is a free piece of software which is available for Mac, Windows and Linux. ![]() There are lots of different styles of “brick” to use and this is a fun way to experiment with different letterforms. How it works: The interface is a grid layout, where you use various styles of “brick” to build letters. Fontstructįormat and price: web-based service free ![]() Regardless of what software you choose, there is a range of ways you can create your own font and I encourage you to try it out! 1. The more expensive ones have a lot more variation in tools, more comprehensive interfaces, and more ability to fine-tune your fonts. The options I present here go from free to cheap to quite expensive. Plus, you create something that can make your digital (and print) environment highly personal. Through the process of making your own fonts, you learn the basics of typography, spacing, and gain an awareness of and appreciation for letter construction. I think font-building is a great skill to have. Making and selling fonts is my main source of income but even if you don’t plan on making a living from it. ![]() ![]() ![]() Follow these steps to toggle a cue from Stream Deck: You need a Stream Deck plug-in for sending OSC messages simply search the Stream Deck Store for “OSC”. OSC (Open Sound Control) is a quick and convenient way to trigger actions in Lightkey. You can use Stream Deck to trigger cues and other actions in Lightkey by means of either OSC or MIDI messages. By default the direction is reversed select the Inverted option to correct this.Įlgato Stream Deck is a popular USB controller which lets you perform various kinds of actions through a grid of freely assignable keys. You can assign an action to the jog wheel in the External Control window. Unfortunately the X-Touch does not send 14-bit fader values in Ctrl mode. You can delete the Note On/Off binding.Assign the action “Change Cue Intensity” to the Control Change binding and choose the desired cue.“D7”) and one for a Control Change command (e.g. Two new MIDI bindings are created: One for a Note On/Off command (e.g. Drag an unassigned fader on the X-Touch.Select “X-Touch INT” from the Input menu.Open the External Control window and then click MIDI.Instead, create the binding in the External Control window: Therefore you can’t use the Add Trigger… command to quickly assign faders to a fader-type button, as Lightkey would identify the control as a button. The faders on the X-Touch send two types of MIDI messages: A Note On message when touching the fader’s knob and CC messages as the fader is being dragged. (If the Ctrl mode is not available you need to update the firmware on your X-Touch controller.) Special Notes Then select the following settings in the configuration menu, as explained in the X-Touch Quick Start Guide: To use a Behringer X-Touch with Lightkey, connect the controller to your Mac with a USB cable. Note: If your MIDI controller offers special feedback options which aren’t supported by Lightkey, you can customize the feedback messages in the External Control window. The following list shows the controllers for which Lightkey currently supports extended feedback. These features are controlled through custom protocols and require special software support. Beyond that, some controllers provide extended feedback options like multi-color LEDs. Lightkey sends MIDI feedback messages to any connected controller, enabling it to reflect the current software state through LEDs, motorized knobs or faders, etc. ![]() ![]() Stupid Zombies 3 is a very fun action arcade game that has nice graphics and a ton of different levels. 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![]() ![]() When you first stop a vehicle, you can call for a backup for your traffic stop. This plugin allows you to more easily call for backup among other things. Ultimate Backup is one of the dependencies for Stop The Ped, one of the best LSPDFR plugins. Using it on an injured citizen or officer allows you to call EMS or tend to them yourself, or if it’s too late call a coroner. Using the context menu on a vehicle allows you to search the vehicle. From here you can perform a search of their person, run an alcohol or drug test, ask more questions, or even arrest them. Once they’re out of the vehicle, you can double-tap the E button by default to stop the ped. You can question the driver, run a breathalyzer or drug swab, or ask them to leave the vehicle. When you’re interacting with a vehicle’s driver, you can use the Stop The Ped context menu to ask for all of the documentation, such as the driver’s license, insurance, and registration. When you pull someone over you can also choose to slow down or completely stop traffic in the area surrounding the traffic stop. When behind vehicles while cruising, the menu allows you to run vehicle checks which give you information about the vehicle’s document status and any flags on the registered owner. Stop The Ped has a crazy amount of features that can be accessed when cruising, during a traffic stop, or on foot through the context menu. This plugin does the job of all three with a better, simpler interface. ![]() You can say goodbye to Smart Radio, Traffic Policer, and Arrest Manager. Stop The Ped does a lot of what other LSPDFR plugins do, but better and with less individual plugins. Along with its dependencies, Ultimate Backup and Compulite, the mod becomes infinitely more immersive. Stop The Ped is a crazy, next-level, plugin and one of the best LSPDFR plugins available right now. Having LSPDFR is not necessary for the functionality of Computer , but it does extend the immersion by adding in a court system. You can also create arrest reports when you arrest the citizens of Los Santos, which adds their case to the court system built into LSPDFR .Īs you may be able to tell already. When used in combination with LSPDFR ’s court system, you can see how your citations play out in court. The ability to write a large number of citations for drivers behaving poorly on the road is incredibly immersive. LSPDFR Computer is one of the best LSPDFR plugins out there. We recommend installing these on a fresh install of LSPDFR without any other plugins, just so there aren’t any issues with duplication. We have collected our five best LSPDFR plugins that you need to download and install. These plugins extend the mod’s functionality and ease of use by a large margin. The base mod is awesome, but the community built around LSPDFR has created a huge amount of plugins. Must be non-negative and less than the size of the collection.LSPDFR is a game-changing mod for Grand Theft Auto V that allows you to take on the role of a first responder, most commonly a law enforcement officer. LSPD First Response: Automatic Roadblocks: Failed to create instance slot, Index was out of range. LSPD First Response: Kiera Bell (S_F_Y_COP_01) was set as a cop LSPD First Response: New cop added without cop data! at () in D:\projects\github\AutomaticRoadblock\AutomaticRoadblock\Instances\InstanceSlot.cs:line 92 at .b_75_0(Vector3 position, Single heading) in D:\projects\github\AutomaticRoadblock\AutomaticRoadblock\Roadblock\Slot\AbstractRoadblockSlot.cs:line 375 at (EBackupUnit unit, Vector3 position) in D:\projects\github\AutomaticRoadblock\AutomaticRoadblock\Lspdfr\LspdfrDataHelper.cs:line 82 at (Ped ped, PedData pedData) in D:\projects\github\AutomaticRoadblock\AutomaticRoadblock\Lspdfr\LspdfrDataHelper.cs:line 197 Must be non-negative and less than the size of the collection.Īt (ExceptionArgument argument, ExceptionResource resource) ![]() |